Mathematics ยท Quantitative Aptitude

Algebraic Expressions and Polynomials

275 Questions

Algebraic expressions and polynomials form the foundation of algebra, involving variables, constants, and mathematical operations. This topic is heavily tested in the quantitative aptitude sections of SSC, banking, and state exams. Use these questions to practice expanding, factoring, and simplifying various polynomial expressions.

Expanding algebraic expressionsFactoring polynomialsAlgebraic identitiesFinding common factorsSimplifying numerical statements

Algebraic Expressions and Polynomials Questions

Multiple choice

Divide (x^4 - 2x^3 + 3x^2 - 4x + 5) by (x - 1).

  1. \(x^3 - x^2 + 2x - 3\)
  2. \(x^3 - x^2 + 2x + 3\)
  3. \(x^3 + x^2 + 2x + 3\)
  4. \(x^3 + x^2 + 2x - 3\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using polynomial long division, we find that the quotient is (x^3 - x^2 + 2x - 3) with a remainder of 2.

Multiple choice

Evaluate the expression: ( 2^3 \cdot 2^5 )

  1. \( 2^6 \)
  2. \( 2^8 \)
  3. \( 2^{10} \)
  4. \( 2^{15} \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the rule of exponents, ( a^m \cdot a^n = a^(m+n) ), we have ( 2^3 \cdot 2^5 = 2^(3+5) = 2^8 ).

Multiple choice

Evaluate the expression: ( 5^0 )

  1. \( 0 \)
  2. \( 1 \)
  3. \( 5 \)
  4. \( 25 \)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Any number raised to the power of 0 is equal to 1. Therefore, ( 5^0 = 1 ).

Multiple choice

Factorize the polynomial x^3 - 2x^2 - 5x + 6.

  1. (x - 1)(x - 2)(x + 3)

  2. (x + 1)(x - 2)(x - 3)

  3. (x - 1)(x + 2)(x - 3)

  4. (x + 1)(x + 2)(x - 3)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We can factorize the polynomial using synthetic division or by grouping terms. By grouping, we have: (x^3 - 2x^2) - (5x - 6) = x^2(x - 2) - 1(x - 2) = (x^2 - 1)(x - 2) = (x - 1)(x + 1)(x - 2).

Multiple choice

What is the name of the chapter in the Bijaganita that discusses geometric figures and their properties?

  1. Kshetravyavahara

  2. Vyavahara

  3. Varga

  4. Ghana
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The chapter in the Bijaganita that focuses on geometric figures and their properties is called 'Kshetravyavahara'.